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Mobility in Symmetry-Regular Bar-and-Joint Frameworks

  • P. W. Fowler
  • S. D. GuestEmail author
  • B. Schulze
Chapter
Part of the Fields Institute Communications book series (FIC, volume 70)

Abstract

In a symmetry-regular bar-and-joint framework of given point-group symmetry, all bars and joints occupy general positions with respect to the symmetry elements. The symmetry-extended form of Maxwell’s Rule is applied to this simplest type of framework and is used to derive counts within irreducible representations for infinitesimal mechanisms and states of self stress. In particular, conditions are given for symmetry-regular frameworks to have at least one infinitesimal mechanism (respectively, state of self stress) within each irreducible representation of the point group of the framework. Similar conditions are found for symmetry-regular body-and-joint frameworks.

Keywords

Infinitesimal rigidity Mechanisms Frameworks Symmetry 

Subject Classifications

52C25 70B15 20C35 

Notes

Acknowledgements

This work was begun during the workshop on Rigidity and Symmetry, held at the Fields Institute, Toronto, October 17–21, 2011, and gained from discussions there with Prof. Stephen Power (Lancaster). PWF thanks the Fields Institute for financial support of his visit.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of SheffieldSheffieldUK
  2. 2.Department of EngineeringUniversity of CambridgeCambridgeUK
  3. 3.Fields InstituteUniversity of TorontoTorontoCanada

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